Imibuzo Eyisibonelo Exoxa Ngezinhlelo Zokungalingani Okuqondile
Uhlelo lokungalingani okuqondile luyigatsha lezibalo elihilela ubudlelwano phakathi kokungalingani okuqondile okuningana. Lolu hlelo luqukethe ukungalingani okubili noma ngaphezulu okudinga ukuxazululwa ukuze kutholakale isethi yesisombululo ehlangabezana nakho konke ukungalingani ngasikhathi sinye. Izingxoxo zezinhlelo zokungalingani okuqondile zivame ukuhlangana nazo ohlelweni lwezifundo zezibalo emazingeni aphansi naphezulu esikoleni samabanga aphezulu, kokubili emibuzweni yezivivinyo kanye nokuzijwayeza kwansuku zonke.
Izinhlelo zokungalingani okuqondile zinezinhlelo zokusebenza eziningi zangempela, kusukela ekusetshenzisweni kahle kwezinsiza kanye nokuhlela ezezimali kuya ekuphathweni kwempahla. Ukuqonda le mibono akubalulekile nje kuphela ekuxazululeni izinkinga zezibalo esikoleni kodwa futhi kulungiselela abafundi ukuxazulula izinkinga zansuku zonke ngokunengqondo nangokuphumelelayo. Ngezansi kunezibonelo zezinkinga kanye nezingxoxo mayelana nezinhlelo zokungalingani okuqondile.
Isibonelo Umbuzo 1
Umbuzo:
Nquma isethi yesisombululo sesistimu elandelayo yokungalingani okuqondile:
\[
\begin{cases}
x + y \leq 6 \\
x – y \geq 2
\ukuphela{amacala}
\]
Ingxoxo:
1. Dweba umugqa womngcele wokungalingani ngakunye:
Ku-\(x + y \leq 6\), sidweba umugqa \(x + y = 6\):
– Uma \(x = 0\), \(y = 6\) iveza iphuzu (0, 6).
– Uma \(y = 0\), \(x = 6\) eveza iphuzu (6, 0).
Ku-\(x – y \geq 2\), sidweba umugqa \(x – y = 2\):
– Uma \(x = 2\), \(y = 0\) iveza iphuzu (2, 0).
– Uma \(y = -2\), \(x = 0\) iveza iphuzu (0, -2).
2. Nquma indawo yokuhlala:
– Umugqa \(x + y = 6\) uwuhlukanisa ube yizifunda ezimbili, bese sihlola iphuzu elilodwa lokuhlola elingekho emgqeni, isibonelo iphuzu (0, 0):
\[
0 + 0 \leq 6 \quad (\text{true})
\]
Ngakho-ke, indawo eyanelisayo ingaphansi noma ngakwesobunxele somugqa \(x + y = 6\).
– Umugqa \(x – y = 2\) uhlukanisa isikrini futhi ngezifunda ezimbili, bese sihlola iphuzu (0, 0):
\[
0 – 0 \geq 2 \quad (\text{false})
\]
Ngakho-ke, indawo eyanelisayo ingaphezulu noma ngakwesokudla komugqa \(x – y = 2\).
3. Thola indawo lapho lezi zifunda ezimbili zihlangana khona:
Isixazululo sohlelo yisifunda esanelisa ukungalingani kokubili. Sifuna indawo yokuhlangana kwezifunda ezimbili ehambisana nesiqondiso sokungalingani ngakunye.
I-Kesimpulan:
Isethi yesisombululo sesistimu yokungalingani okuqondile ingamaphuzu onke ekuxhumaneni kwezifunda ezimbili ezihlangabezana nezimo \(x + y \leq 6\) kanye \(x – y \geq 2\).
Isibonelo Umbuzo 2
Umbuzo:
Nquma isethi yesisombululo sesistimu elandelayo yokungalingani okuqondile ku-quadrant yokuqala:
\[
\begin{cases}
2x + 3y \leq 12 \\
x \geq 0 \\
y \geq 0 \\
\ukuphela{amacala}
\]
Ingxoxo:
1. Dweba umugqa womngcele wokungalingani ngakunye:
Ku-\(2x + 3y \leq 12\), sidweba umugqa \(2x + 3y = 12\):
– Uma \(x = 0\), \(y = 4\) iveza iphuzu (0, 4).
– Uma \(y = 0\), \(x = 6\) eveza iphuzu (6, 0).
2. Nquma indawo yokuhlala:
– Umugqa \(2x + 3y = 12\) kanye nephuzu lokuhlola (0, 0):
\[
2(0) + 3(0) \leq 12 \quad (\text{true})
\]
Ngakho-ke, indawo eyanelisayo ingaphansi noma ngakwesobunxele somugqa \(2x + 3y = 12\).
– \(x \geq 0\) kanye \(y \geq 0\) zibonisa ukuthi iphuzu lesixazululo lisesigabeni sokuqala.
3. Thola indawo lapho lezi zifunda ezimbili zihlangana khona:
Isixazululo sesistimu yindawo esesigabeni sokuqala esingezansi noma ngakwesobunxele somugqa \(2x + 3y = 12\).
I-Kesimpulan:
Isethi yesisombululo sesistimu yokungalingani okuqondile amaphuzu aku-quadrant yokuqala agcwalisa i-\(2x + 3y \leq 12\).
Isibonelo Umbuzo 3
Umbuzo:
Nquma isethi yesisombululo sesistimu elandelayo yokungalingani okuqondile:
\[
\begin{cases}
y \geq 2x – 3 \\
y \leq -x + 1
\ukuphela{amacala}
\]
Ingxoxo:
1. Dweba umugqa womngcele wokungalingani ngakunye:
Ku-\(y \geq 2x – 3\), sidweba umugqa \(y = 2x – 3\):
– Uma \(x = 0\), \(y = -3\) iveza iphuzu (0, -3).
– Uma \(y = 0\), \(x = 1,5\) eveza iphuzu (1.5, 0).
Ku-\(y \leq -x + 1\), sidweba umugqa \(y = -x + 1\):
– Uma \(x = 0\), \(y = 1\) iveza iphuzu (0, 1).
– Uma \(y = 0\), \(x = 1\) eveza iphuzu (1, 0).
2. Nquma indawo yokuhlala:
– Umugqa \(y \geq 2x – 3\) uhlolwe ngephuzu (0, 0):
\[
0 \geq 2(0) – 3 \quad (\text{true})
\]
Ngakho-ke, indawo ehlangabezanayo ingaphezulu noma ngakwesokudla komugqa \(2x - 3\).
– Umugqa \(y \leq -x + 1\) uhlolwe ngephuzu (0, 0):
\[
0 \leq -0 + 1 \quad (\text{true})
\]
Ngakho-ke, indawo egcwalisayo ingaphansi noma ngakwesobunxele somugqa \(-x + 1\).
3. Thola indawo lapho lezi zifunda ezimbili zihlangana khona:
Isixazululo sohlelo yisifunda esanelisa kokubili ukungalingani. Sifuna indawo lapho kuhlangana khona ukungalingani okubili.
I-Kesimpulan:
Isethi yesixazululo sesistimu yokungalingani okuqondile amaphuzu asemgwaqweni wesifunda ahlangabezana ne-\(y \geq 2x - 3\) kanye ne-\(y \leq -x + 1\).
Ngokuqonda indlela yokuxazulula izinhlelo zokungalingani okuqondile, kunethemba lokuthi abafundi bazoba nekhono elithe xaxa ekuxazululeni izinkinga zezibalo nokusebenzisa le mibono ezimweni zansuku zonke. Ngethemba ukuthi lezi zinkinga nezingxoxo zezibonelo zizosiza abafundi bafunde futhi baqonde imiqondo eyisisekelo yezinhlelo zokungalingani okuqondile.
